--- /dev/null
+// Copyright (c) 2006 Xiaogang Zhang
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0. (See accompanying file
+// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#ifndef BOOST_MATH_BESSEL_KN_HPP
+#define BOOST_MATH_BESSEL_KN_HPP
+
+#ifdef _MSC_VER
+#pragma once
+#endif
+
+#include <boost/math/special_functions/detail/bessel_k0.hpp>
+#include <boost/math/special_functions/detail/bessel_k1.hpp>
+#include <boost/math/policies/error_handling.hpp>
+
+// Modified Bessel function of the second kind of integer order
+// K_n(z) is the dominant solution, forward recurrence always OK (though unstable)
+
+namespace boost { namespace math { namespace detail{
+
+template <typename T, typename Policy>
+T bessel_kn(int n, T x, const Policy& pol)
+{
+ T value, current, prev;
+
+ using namespace boost::math::tools;
+
+ static const char* function = "boost::math::bessel_kn<%1%>(%1%,%1%)";
+
+ if (x < 0)
+ {
+ return policies::raise_domain_error<T>(function,
+ "Got x = %1%, but argument x must be non-negative, complex number result not supported.", x, pol);
+ }
+ if (x == 0)
+ {
+ return policies::raise_overflow_error<T>(function, 0, pol);
+ }
+
+ if (n < 0)
+ {
+ n = -n; // K_{-n}(z) = K_n(z)
+ }
+ if (n == 0)
+ {
+ value = bessel_k0(x, pol);
+ }
+ else if (n == 1)
+ {
+ value = bessel_k1(x, pol);
+ }
+ else
+ {
+ prev = bessel_k0(x, pol);
+ current = bessel_k1(x, pol);
+ int k = 1;
+ BOOST_ASSERT(k < n);
+ T scale = 1;
+ do
+ {
+ T fact = 2 * k / x;
+ if((tools::max_value<T>() - fabs(prev)) / fact < fabs(current))
+ {
+ scale /= current;
+ prev /= current;
+ current = 1;
+ }
+ value = fact * current + prev;
+ prev = current;
+ current = value;
+ ++k;
+ }
+ while(k < n);
+ if(tools::max_value<T>() * scale < fabs(value))
+ return sign(scale) * sign(value) * policies::raise_overflow_error<T>(function, 0, pol);
+ value /= scale;
+ }
+ return value;
+}
+
+}}} // namespaces
+
+#endif // BOOST_MATH_BESSEL_KN_HPP
+